A = l x w
π = 3.14
7th
Grade
4 + 6 = 6 + 4
½
= 0.5
% ≈
1.
Natural Numbers (Counting Numbers) are the set of numbers that begin with 1, 2, 3, 4,
etc.
2.
Whole numbers
are the set of numbers that begin with 0, 1, 2, 3, 4, etc.
3.
A whole number that has
more than two factors is a composite
number.
4.
A prime number has exactly two factors, 1 and the number itself.
5.
Writing a composite
number as a product of primes is called prime
factorization.
6.
Integers are
positive and negative whole numbers, including zero.
7.
Positive numbers and
negative numbers are opposites.
8.
The sum of two opposites
is always zero.
9.
Subtracting two integers
can be done by adding it’s opposite.
10.
When multiplying
/dividing two numbers with the same sign, the product / quotient will always be
positive.
11.
When multiplying /
dividing two numbers with different signs, the product / quotient will always
be negative.
12.
A rational number is a number that can be written as a fraction,
where the denominator cannot be zero.
13.
A number that is
represented by a non-repeating, non-terminating decimal is called an irrational number.
14.
When solving a problem
with multiple operations, use the order
of operations PEMDAS: Parenthesis, Exponents, Multiplication or Division
(left to right), Addition or Subtraction (left to right)
15.
The absolute value of a number is the distance between the number and
zero on a number line.
16.
A fraction is a quotient of two numbers where the denominator is not
zero.
17.
The number on the top of
a fraction is called the numerator.
18.
The number on the bottom
of a fraction is called the denominator.
19.
A fraction where the
numerator is greater than the denominator is called an improper fraction.
20.
A mixed number has a whole number and a fraction.
21.
Two fractions that are
equal to each other are called equivalent
fractions.
22.
To add or subtract two
fractions you need to have a common denominator.
23.
The least common denominator (LCD) of two fractions can be found by
finding the lowest common multiple of the two denominators.
24.
Simplifying fractions is dividing the numerator and the denominator by
their greatest common factor (GCF)
25.
The greatest common factor (GCF) of two numbers is the greatest number
that is a factor of both numbers.
26.
When multiplying two
fractions, multiply the two numerators together and the two denominators
together.
27.
To divide two fractions,
multiply the first fraction by the reciprocal of the second fraction.
28.
Two numbers are reciprocals if their product is one.
29.
To convert a fraction to
a decimal, take the numerator divided by the denominator.
30.
A repeating decimal is a decimal in which a digit or a sequence of
digits keeps repeating.
31.
A terminating decimal is a decimal that stops, or terminates.
32.
A percent (%) is a ratio that compares a number to 100.
33.
To convert a decimal to
a percent, multiply the decimal by 100, or
move the decimal point 2 places to the right.
34.
Decimals, percents and
fractions are different ways to write the same number.
35.
A proportion is an equation stating that two ratios are equal.
36.
A ratio is a comparison of two numbers by division.
37.
To solve proportions,
cross multiply and divide.
38.
A base is the number or the variable that is being raised to a power.
39.
An exponent tells you how many times a base is used as a factor.
40.
A power is a number expressed using an exponent.
41.
Scientific Notation is a way of writing very large numbers and very small numbers using
powers of ten.
42.
A perfect square is the product of two identical numbers. 4² = 4 x 4 = 16
43.
The square root of a number is a number which when multiplied by itself
equals the given number.
44.
A radical √ is the
symbol used to denote a square root.
45.
Any number raised to the
zero power equals one. 4º = 1
46.
An expression is a mathematical sentence that contains numbers and /
or variables, separated by operation signs.
47.
An equation is a mathematical sentence showing that two expressions
are equal to each other.
48.
Any value or values that
make an equation true is called a solution.
49.
Inverse operations are operations that undo each other (addition « subtraction; multiplication « division; square « square root)
50.
A symbol, usually a
letter, which stands for a number, is called a variable.
51.
An inequality
is a comparison of two expressions.
52.
< is the symbol for less than.
53.
> is the symbol for greater than.
54.
≤ is the symbol for less than or equal
to
55.
≥ is the symbol for greater than or
equal to.
56.
≠ is the symbol for not equal to.
57.
The associative property of addition and multiplication says that if
numbers are grouped together differently, the expressions will still remain
equal. ( 1 + 2 ) + 3 = 1 + ( 2 + 3 )
and 4 · ( 5 · 6 ) = ( 4 · 5 ) · 6
58.
The commutative property of addition and multiplication says that when
you change the order, the expressions will still remain equal. 7 + 8 = 8 + 7 and 9 · 10 = 10 · 9
59. The distributive
property shows that a · ( b + c ) = a·b + a·c. You multiply “a” by each “b” and by “c”. 2 ( 3 + 4 ) = 2 · 3
+ 2 · 4
60.
The zero property of multiplication states that the product of zero and
any number is zero. 5 · 0 = 0
61.
Data is
information gathered.
62.
Frequency is
the number of times something occurs in a set of data.
63.
The mean (average) of a set of data is the sum of the data divided by
the number of items in the set of data.
64.
The median is the middle number when the data is in numerical order.
65.
The mode of a set of data is the data item that occurs most often.
66.
The range of a set of numerical data is the difference between the
greatest and least values of the set.
67.
A data item that is far
apart from the rest of the data is an outlier.
68.
A histogram is a bar graph that represents frequency of data.
69.
Line graphs
represent how data changes over time.
70.
Circle graphs
are best for comparing parts to a whole
71.
Probability
is used to describe how likely it is that an event will happen. It is the ratio of favorable outcomes to
possible outcomes.
72.
To figure the
probability of an event occurring: P(event) = Number of successful ways for
an event to happen
Total number of possible outcomes
73.
An outcome is a possible result.
74.
Theoretical probability is what “should” happen.
75.
Experimental probability is what “does” happen.
76.
When two events have no
effect on each other they are considered independent
events.
77.
When a second event is
affected by the result of a previous event, it is called dependent events.
78.
A mathematical tool that
is used to measure an angle is called a protractor.
79.
An angle is made up of two rays that share a common endpoint called
the vertex.
80.
An angle that measures
exactly 90 degrees is called a right
angle.
81.
An angle that measures
greater than 90 degrees, but less than 180 degrees is called an obtuse angle.
82.
An angle that measures
less than 90 degrees is called an acute
angle.
83.
Two angles that are side
by side and share a common ray are called adjacent
angles.
84.
Two adjacent angles,
whose measurements add up to 90 degrees, are called complementary angles.
85.
Corresponding angles are created when a transversal intersects two parallel lines.
86.
Vertical angles
are congruent angles formed whenever two lines intersect.
87.
An angle that measures
exactly 180 degrees is called a straight
angle.
88.
Two adjacent angles,
whose measurements add up to 180 degrees are, called supplementary angles.
89.
A straight path that
extends in both directions forever is called a line.
90.
Lines that are in the
same plane that will never intersect are called parallel lines.
91.
Perpendicular lines are lines that intersect to form right angles.
92.
A straight path that
extends in one direction forever is called a ray.
93.
A line that intersects
two parallel lines is called a transversal.
94.
An intersection is where two lines cross.
95.
The common endpoint
where two rays intersect is called the vertex.
96.
A segment is part of a line.
97.
The midpoint of a segment is the point that divides the segment into
two congruent segments.
98.
A circle is a closed curve where all the points are the same distance
from the center.
99.
Half of a circle is
called a semicircle.
100. An arc is part of a circle.
101. A segment that
passes through the center of a circle and has both endpoints on the circle is
called the diameter.
102. A segment that
has one endpoint at the center of a circle and the other endpoint on the circle
is called a radius.
103. A segment that
has both endpoints on the circle is called a chord.
104. A closed plane
figure formed by three or more line segments that do not cross is called a polygon.
105. A regular polygon has all sides congruent
and all angles congruent.
106. A triangle is a polygon with three sides.
107. An equilateral triangle has all equal
sides and equal angles.
108. An isosceles triangle has two equal sides
and two equal angles.
109. A scalene triangle has no equal sides and
no equal angles.
110. The sum of the
angles in a triangle will always equal 180 degrees.
111. Right triangles have one 90-degree angle.
112. Obtuse triangles have one angle more than 90 degrees.
113. Acute triangles have only acute angles.
114. A quadrilateral is a polygon with four
sides.
115. A parallelogram is a quadrilateral that
has two sets of parallel lines.
116. A rectangle is a quadrilateral that has
two sets of parallel lines and four right angles.
117. A rhombus (diamond) is a quadrilateral
that has four congruent sides and no right angles.
118. A square is a quadrilateral with two sets
of parallel lines, four right angles and four congruent sides.
119. A trapezoid is a quadrilateral that has
exactly one pair of parallel sides.
120. The sum of the
angles in a quadrilateral will always equal 360 degrees.
121. A five-sided
polygon is called a pentagon.
122. A hexagon is a polygon with six sides.
123. An eight-sided
polygon is called an octagon.
124. A decagon is a polygon with ten sides.
125. If two figures
are congruent, then they have the
same measurement.
126. Similar shapes have the same shape and angles, but not necessarily
the same size.
127. Pi
(π) is the ratio of the circumference to the diameter of a circle. π = 3.14
128. The number of
square units needed to cover the inside of a figure is called the area.
129. The area of a
rectangle is A = l · w
130. The area of a
triangle is A = ½ · b · h
131. The area of a
square is A = s²
132. The area of a
parallelogram is A = b · h
133. The area of a
circle is A = π · r²
134. The area of a
trapezoid is A = ½ · h · ( b1 + b )
135. Perimeter is the distance around a figure.
136. To find the
perimeter of a polygon, add all sides together.
137. The distance
around a circle is called the circumference.
138. The
circumference of a circle if the radius is known is C = 2 · π · r
139. The
circumference of a circle if the diameter is known is C = π · d
140. The surface area of a prism is the sum of
the areas of the faces.
141. The volume of a three-dimensional figure is
the number of cubic units needed to fill the space inside the figure.
142. The volume of
a prism is V = l · w · h
143. The volume of
a cylinder is V = π · r² · h
144. The Pythagorean Theorem states that in any
right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the
hypotenuse. ( a²
+ b² = c² )
145. The distance
something travels is equal to the rate it travels multiplied by the time it
takes to get there. Distance = Rate · Time (D = R · T)
146. Interest is
the fee that a person pays when they borrow money from a bank.
Interest = Principle · Rate · Time ( I = P · R · T)
147. A horizontal
number line (x-axis) and a vertical number line (y-axis) form a coordinate plane.
148. An ordered pair is a pair of numbers that
describe the location of a point on a coordinate plane.
149. The point of
intersection of the x-axis and the y-axis on a coordinate plane is called the origin.
150. The x-axis and y-axis divide the coordinate plane into
four regions, called quadrants.
Quadrant I (+x, +y); Quadrant II (-x, +y); Quadrant III (-x, - y);
Quadrant IV (+x, -y).
151. A linear equation is an equation that
forms a line.
152. Slope
is a ratio that describes the steepness of a line.
153. A graph that
has a positive slope has a line that goes from Quadrant III to Quadrant
I.
154. A graph that
has a negative slope has a line that
goes from Quadrant II to Quadrant IV.
155. A graph with no slope is a vertical line.
156. A graph with zero slope is a horizontal line.
157. A function is a pairing of two sets of
numbers where for every number in the first set there is only one corresponding
number in the second set.
158. The domain of a function is the x values.
159. The range of a function is the y values.
160. The answer to
an addition problem is called the sum.
161. The answer to
a subtraction problem is called the difference.
162. The answer to
a multiplication problem is called the product.
163. The answer to
a division problem is called the quotient.
164. A Venn diagram is a diagram that
illustrates the relationships between objects or numbers.